In computer science, more specifically in automata and formal language theory, nested words are a concept proposed by Alur and Madhusudan as a joint generalization of words, as traditionally used for modelling linearly ordered structures, and of ordered unranked trees, as traditionally used for modelling hierarchical structures. Finite-state acceptors for nested words, so-called nested word automata, then give a more expressive generalization of finite automata on words.
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Deterministic context-free language
A deterministic context-free language is a formal language which is defined by a deterministic context-free grammar. The set of deterministic context-free languages is called DCFL and is identical to the set of languages accepted by a deterministic pushdown automaton. The set of deterministic context-free languages is a proper subset of the set of context-free languages that possess an unambiguous context free grammar.
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Automata theory
In theoretical computer science, automata theory is the study of mathematical objects called abstract machines or automata and the computational problems that can be solved using them. Automata comes from the Greek word ¿¿¿¿¿¿¿¿ meaning "self-acting". The figure at right illustrates a finite state machine, which belongs to one well-known variety of automaton. This automaton consists of states (represented in the figure by circles), and transitions (represented by arrows).
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Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic uses only variables that range over individuals (elements of the domain of discourse); second-order logic has these variables as well as additional variables that range over sets of individuals.
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Context-free language
In formal language theory, a context-free language is a language generated by some context-free grammar. The set of all context-free languages is identical to the set of languages accepted by pushdown automata.
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Tree automaton
A tree automaton is a type of state machine. Tree automata deal with tree structures, rather than the strings of more conventional state machines. The following article deals with branching tree automata, which correspond to regular languages of trees. For a different notion of tree automaton, see tree walking automaton. As with classical automata, finite tree automata (FTA) can be either a deterministic automaton or not.
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Regular language
In theoretical computer science and formal language theory, a regular language is a formal language that can be expressed using a regular expression. Note that the "regular expression" features provided with many programming languages are augmented with features that make them capable of recognizing languages that can not be expressed by the formal regular expressions (as formally defined below).
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Concatenation
In computer programming, string concatenation is the operation of joining two character strings end-to-end. For example, the strings "snow" and "ball" may be concatenated to give "snowball". In many programming languages, string concatenation is a binary infix operator. For example, the following expression uses the "+" symbol as the concatenation operator to join 2 strings:, and has the value "Hello, World".
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